a: Ta có: \(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+2\right)=15\)

\(\Leftrightarrow x^3+8-x^3-2x=15\)

\(\Leftrightarrow2x=-7\)

hay \(x=-\dfrac{7}{2}\)

b: Ta có: \(\left(x-2\right)^3-\left(x-4\right)\left(x^2+4x+16\right)+6\left(x+1\right)^2=49\)

\(\Leftrightarrow x^3-6x^2+12x-8-x^3+64+6\left(x+1\right)^2=49\)

\(\Leftrightarrow-6x^2+12x+56+6x^2+12x+6=49\)

\(\Leftrightarrow24x=-13\)

hay \(x=-\dfrac{13}{24}\)

\(\left(x+4\right)\left(x^2-4x+16\right)-\left(x-2\right)\left(x^2+2x+4\right)\)

\(=x^3-4x^2+16x+4x^2-16x+64-\left(x^3+2x^2+4x-2x^2-4x-8\right)\)

\(=x^3+\left(-4x^2+4x^2\right)+\left(16x-16x\right)+64-\left(x^3-8\right)\)

\(=x^3+0+0+64-x^3+8\)

\(=\left(x^3-x^3\right)+\left(64+8\right)\)

\(=0+72=72\)

(x + 4)(x² - 4x + 16) - (x - 2)(x² + 2x + 4)

= x³ + 4³ - (x³ - 2³)

= x³ + 64 - x³ + 8

= 72

1: =>x^2+4x-21=0

=>(x+7)(x-3)=0

=>x=3 hoặc x=-7

2: =>(2x-5-4)(2x-5+4)=0

=>(2x-9)(2x-1)=0

=>x=9/2 hoặc x=1/2

3: =>x^3-9x^2+27x-27-x^3+27+9(x^2+2x+1)=15

=>-9x^2+27x+9x^2+18x+9=15

=>18x=15-9-27=-21

=>x=-7/6

6: =>4x^2+4x+1-4x^2-16x-16=9

=>-12x-15=9

=>-12x=24

=>x=-2

7: =>x^2+6x+9-x^2-4x+32=1

=>2x+41=1

=>2x=-40

=>x=-20

a) Rút gọn được VT = 9x + 7. Từ đó tìm được x = 1.

b) Rút gọn được VT = 2x + 8. Từ đó tìm được x = 7 2 .